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How do I solve:
lim [(x^2-2x+1)cos(1/x^2-1)]=0
x-1
lim [(x^2-2x+1)cos(1/x^2-1)]=0
x-1
The Squeeze Theorem, also known as the Sandwich Theorem or the Pinching Theorem, is a mathematical theorem used to find the limit of a function using two other functions that "squeeze" the original function between them.
The Squeeze Theorem states that if two functions, g(x) and h(x), are both approaching the same limit as x approaches a certain value, and a third function, f(x), is always between g(x) and h(x), then f(x) will also approach the same limit as x approaches that value.
In order to use the Squeeze Theorem to solve a limiting value, you must first identify two functions that are approaching the same limit as the original function. Then, show that the original function is always between these two functions. Finally, use the limit of the two known functions to determine the limit of the original function.
The main advantage of using the Squeeze Theorem is that it can be used to solve limits that are otherwise difficult or impossible to solve using other methods. It is particularly useful for finding the limit of a function as it approaches infinity or negative infinity.
While the Squeeze Theorem can be a very useful tool in solving limiting values, it does have its limitations. It can only be used when there are two other functions that are approaching the same limit as the original function, and it can only be used to find the limit as x approaches a specific value, not the value itself.